Database

[{item:"journal",qty:25,tags:["blank","red"],dim_cm:[14,21]},{item:"notebook",qty:50,tags:["red","blank"],dim_cm:[14,21]},{item:"paper",qty:100,tags:["red","blank","plain"],dim_cm:[14,21]},{item:"planner",qty:75,tags:["blank","red"],dim_cm:[22.85,30]},{item:"postcard",qty:45,tags:["blue"],dim_cm:[10,15.25]}]

Query

db.collection.aggregate([{$project:{_id:0,arr:{"$concatArrays":[{$map:{input:"$tags",as:"item",in:{k:"tag",v:"$$item"}}},{$map:{input:"$dim_cm",as:"item",in:{k:"dim_cm",v:"$$item"}}}]}}},{$unwind:"$arr"},{$group:{_id:null,tags:{$addToSet:{$cond:[{$eq:["$arr.k","tag"]},"$arr.v","$$REMOVE"]}},dim_cm:{$addToSet:{$cond:[{$eq:["$arr.k","dim_cm"]},"$arr.v","$$REMOVE"]}}}}])

Result